Fundamentally, a hash is a data structure optimized for solving the converse question, knowing whether the key 2 is present. But it's hard to judge without knowing, so let's assume that won't change.

Possibilities presented here will depend on:

how often you need to do it

how dynamic the hash is

One-time op

grep $_==2, values %x (also spelled grep {$_==1} values %x) will return a list of as many 2s as are present in the hash, or, in scalar context, the number of matches. Evaluated as a boolean in a condition, it yields just what you want.grep works on versions of Perl as old as I can remember.

use List::Util qw(first); first {$_==2} values %x returns only the first match, undef if none. That makes it faster, as it will short-circuit (stop examining elements) as soon as it succeeds. This isn't a problem for 2, but take care that the returned element doesn't necessarily evaluate to boolean true. Use defined in those cases.List::Util is a part of the Perl core since 5.8.

use List::MoreUtils qw(any); any {$_==2} values %x returns exactly the information you requested as a boolean, and exhibits the short-circuiting behavior.List::MoreUtils is available from CPAN.

2 ~~ [values %x] returns exactly the information you requested as a boolean, and exhibits the short-circuiting behavior.Smart matching is available in Perl since 5.10.

Repeated op, static hash

Construct a hash that maps values to keys, and use that one as a natural hash to test key existence.

my %r = reverse %x;
if ( exists $r{2} ) { ... }

Repeated op, dynamic hash

Use a reverse lookup as above. You'll need to keep it up to date, which is left as an exercise to the reader/editor. (hint: value collisions are tricky)